‎A rank equality is established for the sum of finitely many tripotent matrices via elementary block matrix operations‎. ‎Moreover‎, ‎by using this equality and Theorems 8 and 10 in [Chen M‎. ‎and et al‎. ‎On the open problem related to rank equalities for the sum of finitely many idempotent matrices and its applications‎, ‎The Scientific World Journal 2014 (2014)‎, ‎Article ID 702413‎, ‎7 pages‎.]‎, ‎some other rank equalities for tripotent matrices are given‎. ‎Furthermore‎, ‎we obtain several rank equalities related to some special types of matrices‎, ‎some of which are available in the literature‎, ‎from the results established‎.

M. Chen, Q. Chen, Q. Li and Z. Yang, On the open problem related to rank equalities for the sum of finitely many idempotent matrices and its applications, The Scientific World Journal 2014 (2014), Article ID 702413, 7 pages.